A fair die is cast until a 6 appears. What is the probability that it must be
cast more than five times?
Bowl 1 contains 6 red chips and 4 blue chips. Five of these 10 chips are
selected at random and without replacement and put into bowl 2, which
was originally empty. One chip is then drawn at random from bowl 2.
Relative to the hypothesis that this chip is blue, find the conditional
probability that 2 red chips and 3 blue chips are transferred from bowl 1 to
bowl 2.
Let the random variable X be normally distributed with μ = 1 and
σ = 2 , compute the probability P(1 < X2 < 9) . Note that P(X < 2) =
0.9772.
Let X have a Poisson distribution with μ = 25 .
(1) Find the moment-generating function of X .
(2) Use Chybyshev’s inequality to determine a lower bound for
P(15 < X < 35) .
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